Homogenization of the G-equation: a metric approach

Antonio Siconolfi ()
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Antonio Siconolfi: Università degli Studi di Roma “La Sapienza”

Partial Differential Equations and Applications, 2021, vol. 2, issue 4, 1-18

Abstract: Abstract The aim of the paper is to recover some results of Cardaliaguet–Nolen–Souganidis in Cardaliaguet et al. (Arch Rat Mech Anal 199(2): 527–561, 2011) and Xin–Yu in Xin and Yu (Commun Math Sci 8(4): 1067–1078, 2010) about the homogenization of the G-equation, using different and simpler techniques. The main mathematical issue is the lack of coercivity of the Hamiltonians. In our approach we consider a multivalued dynamics without periodic invariants sets, a family of intrinsic distances and perform an approximation by a sequence of coercive Hamiltonians.

Keywords: Homogenization; Hamilton–Jacobi equations; Effective Hamiltonian; 35B40; 35F21; 37J99; 49L25 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00097-5

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